by Karen Hunger Parshall
© Oxford University Press 2004 All rights reserved
Sylvester, James Joseph (1814-1897), mathematician, was born on 3 September 1814 in London, the youngest son of five sons and four daughters of Abraham Joseph, merchant. Two of his older brothers emigrated to the United States and adopted the surname Sylvester, a convention which he and at least one other brother followed. Between the ages of six and twelve he studied at the boarding-school run by Neumegen in Highgate, where he so distinguished himself in mathematics that Olinthus Gregory, professor of mathematics at the Royal Military Academy, Woolwich, was asked to evaluate his mathematical abilities further. Gregory recognized real talent in the boy and urged that particular attention be paid to his subsequent mathematical training. Sylvester proceeded to Daniell's boarding-school in Islington before entering London University in its opening year of 1828.
London University presented the fourteen-year-old boy with prime opportunities: the school's non-sectarian policies allowed Sylvester, a Jew, not only to learn but also to take a degree, and its professor of mathematics was the gifted Augustus De Morgan. Unfortunately, Sylvester studied there for only five months before his family withdrew him following an incident in the refectory in which he allegedly assaulted a fellow student with a table knife. In 1829 he was sent to live with aunts in Liverpool and to attend the Royal Institution School there. Although he once again distinguished himself in mathematics, winning the school's first prize in the subject, as well as a $500 prize from the contractors of lotteries of New York for the solution of a combinatorial problem, he was so unhappy in Liverpool that he ran away to Dublin. Quite by chance a member of the family discovered him there and returned him to England.
Sylvester was next entered as a sizar at St John's College, Cambridge, on 7 July 1831, matriculating officially four months later on 14 November. Illness interrupted his stay at Cambridge twice between June 1833 and 19 January 1836, when he was readmitted as a pensioner. In January 1837 he was second wrangler in the mathematical tripos, but, as a non-Anglican, he could not subscribe to the Thirty-Nine Articles of the Church of England and so could neither take his degree nor compete for further prizes or fellowships. (Cambridge would eventually award him the degrees of BA and MA honoris causa in 1872 following the repeal of the Test Acts, and made him an honorary ScD in 1890; Oxford made him a DCL in 1880.)
With Cambridge and Oxford closed to him at graduate level in the late 1830s, Sylvester won the professorship of natural philosophy at University College, London, in 1838. This should have been another prime opportunity for him, in light of the paucity of higher level teaching positions available in England for non-Anglicans, but he found the duties of the post uncongenial and resigned in 1841 to take the professorship of mathematics at the University of Virginia, founded in Charlottesville by Thomas Jefferson in 1819. His short tenure at University College had not been uneventful, however: his early papers on topics in mathematical physics had secured him a fellowship in the Royal Society in 1839; he had proven his first mathematical result in the algebraic theory of elimination (1840), a subject which would ultimately lead him to his seminal research in the theory of invariants; and he had officially earned both the BA and the MA from Trinity College, Dublin, in 1841.
In November 1841 the short, burly, and bespectacled Englishman with the cockney accent arrived in central Virginia, somewhat late for the academic term, to begin his duties teaching mathematics to young men from wealthy southern families. Although initially welcomed warmly into the university community, Sylvester soon found himself at odds with at least one disrespectful student in his classroom. At the end of February 1842 he called on the faculty senate to expel the student for insubordination. When the senate officially disciplined the student but did not expel him (perhaps fearing a recurrence of the student unrest that had, less than two years before, resulted in the murder of a member of the faculty), Sylvester protested at the decision and ultimately resigned his position in March 1842.
Sylvester left Charlottesville for his brother's home in New York city, and tried in vain to secure another academic position in the United States. He also met with the refusal--on religious grounds--of his proposal of marriage to a Miss Marston of New York. (He would never marry and had no children.) Thoroughly disheartened, he returned to England late in November 1843 to face uncertain prospects.
By December 1844 Sylvester had 'recovered [his] footing in the world's slippery path' (Sylvester to Joseph Henry, 12 April 1846, Smithsonian Institution, Henry MSS, M099, no. 8573) and had taken posts as secretary and actuary at the Equity and Law Life Assurance Company in London. Two years later, in 1846, he had also entered the Inner Temple to prepare himself for a career in law but, while he was called to the bar in 1850, he never practised. At some time during his four years of legal training, he met another misplaced mathematician studying for the bar, Arthur Cayley. This meeting developed into both a lifelong friendship and the sustained mathematical dialogue that would produce the field of invariant theory, an area of pure mathematics with deep applications in geometry as well as physics.
After publishing very little in the 1840s Sylvester truly came into his own as a mathematical researcher in the 1850s. Extending his work in elimination theory to an analysis of the determinants per se that arose in that research, he sought to develop what he termed in 1851 a 'general theory of associated forms'. This quickly led him to a study of the invariantive properties of such forms. In 1852 he began the process of creating a theory of invariants from numerous isolated results, in his massive paper 'On the principles of the calculus of forms' (Cambridge and Dublin Mathematical Journal, 7, 1852; 8, 1853). Among other things, this involved determining techniques for calculating explicitly the invariants of a given form and for exploring the interrelations between those invariants. His assault on the latter set of issues resulted in another mammoth paper the following year on the very sticky problem of detecting algebraic dependence relations, or 'syzygies' (the term he coined) among invariants. This paper also provided a dictionary of the evolving language of invariant theory that he gloried in creating out of his extensive knowledge of French, German, Italian, Latin, and classical Greek.
Concurrent with this mathematical research Sylvester carried out his actuarial work at Equity Law and Life with distinction, compiling a 'Table of whole life assurances with profits; annual premium for an assurance of 100 pounds' which was still in use by the society for ages twenty-five and older as late as 1923. He also founded the Law Reversionary Interest Society Ltd and served as its first actuary (1853-5). Despite these professional successes Sylvester had tired by the mid-1850s of his dual existence as actuary and research mathematician and tried, unsuccessfully, in 1854 for the vacant professorship of mathematics at the Royal Military Academy in Woolwich. When the new incumbent died shortly after assuming his duties, Sylvester reapplied, and this time won the post, which he held from 1855 to 1870.
Sylvester's first ten years at Woolwich proved fruitful and rewarding. He continued his research in invariant theory, made new breakthroughs in the not unrelated combinatorial field of partition theory (1859), and gave the first rigorous proof of Newton's rule for locating the imaginary roots of a polynomial equation (1864). His achievements also received significant recognition in the form of the Royal Society's royal medal in 1861 and the title of foreign correspondent to the French Académie des Sciences in 1863. Socially, he participated actively and regularly at the Athenaeum, the club of which he became a member in 1856. The last five Woolwich years, however, found him mathematically unfocused and increasingly at odds with the military authorities over his teaching load. Not even the second presidency, in 1866, of the new London Mathematical Society, nor the presidency of the mathematics and physics section of the British Association for the Advancement of Science at its 1869 meeting in Exeter served to soften the blow inflicted when a change in the regulations forced his premature retirement at the age of fifty-five and denied him a full pension.
The publication of Sylvester's only book, The Laws of Verse (1870), coincided with this bitter turn of events; indeed, it was not mathematics but poetry, a try for a seat on the London school board, and life at his club that largely occupied him from 1870 to 1875. These years saw the publication of only eight short and uninspired mathematical articles by the previously prolific and profound Sylvester. In 1875, however, he found himself under serious consideration for the professorship of mathematics at the newly forming Johns Hopkins University in Baltimore, Maryland. Under the direction of its first president, Daniel Coit Gilman, Johns Hopkins was to be the first research-orientated university in the United States, one which emphasized both undergraduate and graduate teaching while it stressed original research and the active training of future researchers. Sylvester won the appointment, made yet another transatlantic move, and assumed his duties when the school opened in 1876.
The years at Johns Hopkins from 1876 to the end of 1883 marked a key phase in Sylvester's life and in the development of research-level mathematics in America. The opportunity to build a programme in mathematics, to teach talented advanced students, and to do his own research in a supportive institutional environment thoroughly re-energized Sylvester. This sense of revitalization comes out with characteristic exuberance and hyperbole in the address that he delivered in 1877 at the commemoration day celebration at Johns Hopkins. He proclaimed to his audience that:
The Johns Hopkins years also witnessed more official recognition for Sylvester from the broader scientific community. In 1880 he received the Copley medal of the Royal Society and in 1883 he was named foreign associate of both the Accademia dei Lincei in Rome and the National Academy of Sciences in the United States. He would later win the De Morgan gold medal from the London Mathematical Society in 1887. Despite such commendation, by the summer of 1883 Sylvester felt increasingly tired and overwhelmed by the pressures of 'the responsibility of directing and molding the mathematical education of 55 million of one of the most intellectual races of men upon the face of the earth' (Sylvester to Felix Klein, 17 Jan 1884, Klein Nachlass XXII L, Niedersächsische Staats- und Universitätsbibliothek, Göttingen). He was also homesick for England and so had applied for the vacant Savilian professorship of geometry at Oxford. He tendered his resignation at Johns Hopkins in September 1883, effective 1 January 1884, despite the fact that the outcome at Oxford was then as yet unknown, was named to the Savilian chair in December, and sailed for England just before the end of the year. The autumn of 1884 found him settled in his rooms in New College, Oxford, and casting about in frustration for a topic for his inaugural lecture. After postponing the lecture due to the lack of a suitable theme, he gave it in December 1885 on a new topic in the theory of invariants--differential invariants, or reciprocants in his terminology--which he had begun to develop over the spring and summer of 1885. This would be his last major mathematical achievement, although he would continue to work intermittently on problems in invariant theory, in combinatorics, and on the Euler-Goldbach conjecture (1897) in number theory up until his death.
Sylvester's health began to fail in the early 1890s, with cataracts presenting the greatest difficulties. A deputy was appointed to perform the duties of his chair for him in 1892, and he officially resigned in 1894. He spent his final years living in and around London with the Athenaeum as his social focal point. He died at his home, 5 Hertford Street, Mayfair, on 15 March 1897 of cardiac failure, having suffered a stroke a fortnight earlier. He was buried on 19 March 1897 in the Jewish cemetery in Ball's Pond, Dalston. The Royal Society honoured his memory with the establishment of its Sylvester medal, an award 'for the encouragement of mathematical research irrespective of nationality, and not confined to pure mathematical research', given triennially from 1901 onward.
KAREN HUNGER PARSHALL
Sources
R. C. Archibald, 'Material concerning James Joseph Sylvester', Studies and essays in the history of science and learning offered in homage of George Sarton (1947), 209-17
R. C. Archibald, 'Unpublished letters of James Joseph Sylvester and other new information concerning his life', Osiris, 1 (1936), 85-154
H. F. Baker, 'Biographical notice', in The collected mathematical papers of James Joseph Sylvester, ed. H. F. Baker, 4 vols. (1904-12); repr. with corrections [1973]
H. H. Bellot, University College, London, 1826-1926 (1929)
L. Feuer, 'America's first Jewish professor: James Joseph Sylvester at the University of Virginia', American Jewish Archives, 36 (1984), 151-201
P. A. MacMahon, 'James Joseph Sylvester', Nature, 55 (1896-7), 492-4
K. H. Parshall, 'America's first school of mathematical research: James Joseph Sylvester at Johns Hopkins University', Archive for History of Exact Sciences, 38 (1988), 153-96
K. H. Parshall, James Joseph Sylvester: life and works in letters (1998)
K. H. Parshall and D. E. Rowe, The emergence of the American mathematical research community, 1876-1900: J. J. Sylvester, Felix Klein, and E. H. Moore (1994)
I. Grattan-Guinness, 'The Sylvester medal: origins, and recipients, 1901-1949', Notes and Records of the Royal Society, 47 (1993), 105-8
Nature, 55 (1896-7), 492-4
Archives
Brown University, Providence, Rhode Island, John Hay Library, letters
St John Cam., corresp. and papers | BL, letters to Charles Babbage, Add. MSS 37189-37199, passim
Col. U., Rare Book and Manuscript Library, letters to W. J. C. Miller, etc.
CUL, corresp. with Lord Kelvin
CUL, letters to Sir George Stokes
Johns Hopkins University, Baltimore, Daniel Coit Gilman MSS
L. Cong., letters to S. Newcomb
Makarna Mittag-Lefflers Matematiska Stiftelse, Djursholm, letters to M. G. Mittag-Leffler
Royal Institution of Great Britain, London, letters to John Tyndall
UCL, letters to Lord Brougham; letters to Edith Gigliucci; letters to Thomas Hirst
UCL, London Mathematical Society papers
University of Exeter Library, letters to Sir Joseph Lockyer
W. Sussex RO, letters to Sir Alfred Kempfe
Likenesses
G. Patten, oils, 1841, priv. coll.
A. E. Emslie, oils, 1889, St John Cam. [see illus.]
A. E. Emslie, oils, second version, New College, Oxford
G. J. Stodart, stipple (after photograph by Messrs J. Stilliard & Co., Oxford), NPG; repro. in Nature, 39 (1889)
Wealth at death
£2730 2s. 8d.: probate, 12 April 1897, CGPLA Eng. & Wales
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